$M/m\ge\sqrt{3}$.

Asked Apr 28 '18 at 17:51

Active Apr 28 '18 at 17:51

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Suppose there are six distinct points in the plane. Let $m$ and $M$ be the minimum and maximum distances among the al possible distances between pairs of points. I have to show $M/m\ge\sqrt{3}$.

I have tried placing the points on the plane in an extremal fashion, but couldn't figure out how to derive such inequality.

asked Apr 28 '18 at 17:51

QED

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Also related: https://math.stackexchange.com/questions/379082/simple-geometry-problem-on-distribution-of-points-in-a-plane. – Martin R Apr 28 '18 at 17:58

$M/m\ge\sqrt{3}$.

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